On the Self-Similar Nature of Ethernet Traffic

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On the Self-Similar Nature of Ethernet Traffic

• - Leland, et. Al
• Presented by
• Sumitra Ganesh

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Overview

• Demonstrate the self-similar nature of Ethernet
  LAN traffic
• Study the degree of self-similarity in various
  data sets using the Hurst parameter as a measure
  of burstiness
• High resolution data collected over several years
  and across several networks
• Discusses models for traffic sources, methods for
  measuring self-similarity and simulating
  self-similar traffic.

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Structure of presentation

• Traffic Measurements
• Self-Similar Stochastic Processes
• Analysis of Ethernet Traffic Measurements
• Source Models
• Implications and Conclusions
• Comments

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Traffic Measurements

• Traffic monitor records for each packet a
  timestamp (accurate to within 100-20 microsec,
  packet length, header information
• Study conducted from 1989-1992
• Network underwent changes during this period
• Data sets with External traffic analyzed
  separately

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Relevant Network Changes

• Aug 89/Oct 89 host to host workgroup traffic
• Jan 1990 host-host and router-to-router
• Feb 1992 predominantly router-to-router traffic

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Self-similarity

• Slowly Decaying Variances Variance of the
  sample mean decreases slower than the reciprocal
  of the sample size.
• Long Range Dependence The autocorrlations decay
  hyperbolically rather than exponentially.
• Power Law Spectral density obeys a power law
  near the origin

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Hurst parameter
For a given set of observations
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Mathematical Models

• Fractional Gaussian noise rigid correlation
  structure
• ARIMA processes more flexible for simultaneous
  modeling of short-term and long-term behavior
• Construction by Mandelbrot aggregation of
  renewal reward processes with inter-arrival times
  exhibiting infinite variances

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Estimating the Hurst parameter H

• Time domain analysis based on the R/S statistic
  robust against changes in the marginal
  distributions
• Analysis of the variances for the aggregated
  processes
• Periodogram based Maximum Likelihood Estimate
  analysis in the frequency domain yields
  confidence intervals

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Ethernet traffic (27 hour)

• Compare variance-time plot, R/S plot and
  periodogram for number of bytes during normal
  hour in Aug 89. H is approx. 0.8
• Estimate is constant over different levels of
  aggregation
• Conclusion The Ethernet traffic over a 24-hour
  period is self-similar with the degree of
  self-similarity increasing as the utilization of
  the Ethernet increases.

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• R/S plot
• Variance-time
• Periodogram
• Different levels
• Analysis for data set
• AUG89.MB

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Four Year period

• Estimate for H is quite stable (0.85-0.95)
• Ethernet traffic during normal traffic hours is
  exactly self-similar
• Estimates from R/S and variance-time plots are
  accurate

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(a)-(d) Aug 89, Oct 89, Jan 90, Feb 92. Analysis
for packet count Normal hour traffic
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• packet count
• - number of bytes
• Low-Normal-High for each

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Observations (4-year)

• H increases from low to normal to high traffic
  hours
• As number of sources increased the aggregate
  traffic does not get smoother rather the
  burstiness increases
• Low traffic hours gets smoother in 90s because
  of router-to-router traffic
• Confidence intervals wider for low traffic hours
  process is asymptotically self-similar

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External Traffic

• Normal/High H is slightly smaller
• Low traffic hours H is 0.55 and confidence
  interval contains 0.5. Therefore coventional
  short-range Poisson based models describe this
  traffic accurately
• 87 of the packets were TCP

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Source Model

• Renewal reward process in which the inter-arrival
  times are heavy-tailed
• With relatively high probability the
  active-inactive periods are very long
• The heavier the tail -gt the greater the
  variability -gt Burstier the traffic
• Not analyzed the traffic generated by individual
  Ethernet users.

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Conclusions

• Ethernet LAN traffic is statistically
  self-similar
• Degree of self-similarity (the Husrt parameter H)
  is typically a function of the overall
  utilization of the Ethernet
• Normal and Busy hour traffic are exactly
  self-similar. Low hour traffic is asymptotically
  self-similar
• External traffic / TCP traffic share the same
  characteristics
• Conventional packet traffic models are not able
  to capture the self-similarity

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Implications

• Congestion ?
• Queueing ?

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Comments

• Convincing analysis and interpretation of results
• Poor graphs for a paper that relies on them so
  heavily